From the AAdvantage MileUp Mastercard® landing page:

"Double miles on grocery store purchases Earn 2 AAdvantage miles for each $1 spent on purchases at grocery stores. Grocery stores are classified as supermarkets, freezer/meat locker provisioners, dairy product stores, miscellaneous food/convenience stores, markets, specialty vendors, and bakeries. Certain non-qualifying purchases: You won’t earn double miles for purchases at general merchandise/discount superstores, wholesale/warehouse clubs, candy/confectionery stores, cafes, bars, lounges, and fast food restaurants."

Sounds to me like Trader Joe's would count (depending on what type of merchant they code themselves as), but that Target would not.